Used in MMORPGs, DPS stands for Damage Per Second, and has two meanings. 1) As an adjective, it describes how much damage a weapon or spell does each second. 2) As a noun, it refers to a character class or specialization which focuses on doing a lot of damage quickly, or in bursts.

1) A dagger has a rating of 112 DPS. That means that the damage it causes per hit, divided by the time it takes to swing with it, comes out to 112.
2) Mages, Rogues, Rangers, and the like focus on dealing a lot of damage, as opposed to tanks who take damage, or healers, who heal damage. Therefore, they are referred to as DPS classes